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Abstract

One of the well-known topics of decision making is Multi-Criteria Decision Making (MCDM). Fuzzy set theory helps to provide a useful way to address a MCDM problem. Without models, MCDM methods cannot be practiced effectively, therefore, it is interesting to clarify the structure among criteria. But the shortcoming of MCDM is unable to capture imprecision or vagueness inherent in the information. Fuzzy set theory has great potential to handle such situations and fuzzy structural models have been developed. In this chapter widely used structural models i.e. Interpretive Structural Modeling (ISM), Decision Making Trial and Evaluation Laboratory (DEMATEL), and Cognition Maps (CMs) are first summarized briefly along with their mathematical formulation and then diffusion these models into fuzzy set theory is explained along with a literature review of the based applications of these models in the digital marketplace.

Fuzzy Set Theory

The substantial universe there is a number of situations where uncertainty can find in information (Zadeh, 1965). When decision-making in a fuzzy environment, the result of decision making is greatly affected by subjective ratings that are obscure and vague. There are many ways of imprecision includes unquantifiable, incomplete information, the information cannot be obtained, and the partial ignorance (Chen et al., 1992). To cope with this type of problem vague and imprecise and manage these problems mathematically, in year of 1965, Zadeh has come with the concept of fuzzy set theory. In this theory, each number indicates a partial truth while crisp sets correspond to the binary logic 0 or 1 (Zadeh, 1965). To address the vagueness of feeling and expression in human decision-making, fuzzy set theory is really useful (Zadeh, 1965). Some important concepts of fuzzy are described:

Def.1: A fuzzy set of the universe of discourse X is Convex if , where..

Def.2:. A fuzzy set of the universe of discourse X is convex if max . = 1.

Def.3: The -cut of the fuzzy set of the universe of discourse X is defined as = where.

Def.4: A triangular fuzzy number can be defined as a triplet (l, m, r), and the membership function is defined as: